We conclude by the fractional Gagliardo-Nirenberg inequality (see e.g. [1]}, [2]} and references therein) and the Sobolev inequality that,
\(\begin{aligned}\Vert \Lambda ^{s} u\Vert _{L^{{p-2}}(\mathbb {R}^{3})}\le C\Vert \nabla u\Vert ^{{2-s-p}}_{L^{p}(\mathbb {R}^{3})}\Vert u\Vert ^{{2-s-p}}_{L^{{2-s}}(\mathbb {R}^{3})}\le C\Vert \nabla u\Vert ^{{2-s-p}}_{L^{p}(\mathbb {R}^{3})}\Vert \Lambda ^{s}u\Vert ^{{2-s-p}}_{L^{2}(\mathbb {R}^{3})},\end{aligned}\) 
